Yes. Limbs are structural elements in a tree; i.e. the bigger branches.

You are correct. Just for fun, you might enjoy searching YouTube for a children's song in English, entitled "The Green Grass Grew All Around." It's an "accumulative rhyme," it gets longer and longer with each verse. It uses words for different parts of a tree. People like to sing the last verse very quickly, all in one breath. Because it's a folk song, the exact words vary. The words I learned, as a kid, were. Ohhhhhhhhhhhhhhhhh... (Deep breath) The feather's on the wing And the wing's on the bird And the bird's on the egg And the egg's in the nest And the nest's on the twig And the twig's on the branch And the branch is on the limb And the limb's on the tree And the tree's on the root And the root's in the hole And the hole's in the ground And the green grass grew all around and around And the green grass grew all around!